Mr Obama made the diplomatic gaffe during a ceremony at the White House, honouring a Polish resistance hero who was among the first to warn the Allies of the systematic slaughter in the Nazi concentration camps.

In an extraordinary reprimand from a European leader to an American president, Prime Minister Donald Tusk said Mr Obama said "offended all Poles" with his words.

"When someone says 'Polish death camps,' it is as if there were no Nazis, no German responsibility, as if there were no Hitler," Mr Tusk said.

"We cannot accept such words even if they are spoken by the leader of a friendly power ... since we expect diligence, care, and respect from our friends on issues of such importance as World War II remembrance."

Mr Tusk rejected a statement of regret by Tommy Vietor, the White House National Security Council spokesman, insisting on a "stronger reaction" from Mr Obama himself.

He also appealed to the President to remember his own great uncle, who served in the US Army during the war and was among the American soldiers who liberated the Buchenwald concentration camp.

Radek Sikorski, the Polish foreign minister, was more blunt. In a late-night message on Twitter he accused the White House of "ignorance and incompetence" and demanded an apology for the "outrageous error".

President Bronislaw Komorowski, the Polish head of state, also said he would write a letter to his American counterpart to express his dismay over his comments.

The furious reaction from Poland's leaders reflects the country's sensitivity to any implication that it was involved in the Holocaust.

Successive Polish governments have adopted a policy of aggressively challenging journalists or foreign politicians who use the phrase "Polish death camps", accurately pointing out that the camps were run by occupying German forces.

Karski, who died in 2000, was a Polish army officer who evaded German forces to gain information on the Nazi treatment of Jews and escaped with the first detailed evidence of the Holocaust.

In his tribute at the White House ceremony, Mr Obama said: "Before one trip across enemy lines, resistance fighters told him that Jews were being murdered on a massive scale, and so he smuggled him into the Warsaw Ghetto and a Polish death camp to see for himself."

Alex Storozynski, president of the influential Kosciuszko Foundation, a Polish-American organisation, said "Karski would have cringed if he heard this."

"The president must acknowledge his mistake and apologise for it. He must do it for Karski and the other Poles that risked their lives trying to stop the Holocaust." he told ABC News.

While Poland remains a staunch US ally – and has 2,500 troops in Afghanistan, making it the sixth-largest international contributor – relations between its government and the Obama administration have often been strained.

Some in Poland felt betrayed by Mr Obama's decision to abandon George W Bush's plans for a European missile defence shield, which would have been based in Poland and the Czech Republic.

Conservatives in both the US and Poland said the White House had caved in to Russia, which furiously opposed the missile shield.